The footage clearly does NOT show any nuclear explosions. It's huge but "conventional" explosions using chemical explosives.
Diagrams show a series of underground chambers which are to be filled with explosives, the access holes plugged with concrete. Footage shows a liquid explosive (presumably nitromethane) being pumped into the ground. The charges are detonated together, the row-charge explosion shown in real time and in slow motion and from several angles.
Various views of the enormous crater are shown, from various angles including aerial, with people in some scenes making its dimensions evident.
Other craters are shown from the air, and an explosion which appears to be a single charge.
I realized this must be documented someplace on the Net, and indeed it is:
"Project DUGOUT consisted of the simultaneous detonation of five, 20-ton, chemical, row-charge explosives in hard, dry rock. The primary purpose of the project was to increase the knowledge of row cratering dimensions in hard, dry rock."
"Descriptors : *NUCLEAR EXPLOSIONS, CRATERING, BASALT, SIMULATION, DEBRIS, SOIL MECHANICS."
Apparently the row-charge test was intended to contribute to preparations for "Project Buggy" which was "the first nuclear row-charge experiment in the Plowshare Program."
A relevant DOE film clip: "Excavating with Nuclear Explosives and Plowshare"
Lots of real nuclear clips:
As for Dugout, nuclear or not (and it's not), I rate it four stars. Impressive blast, fun to watch. Dry and soundless (was its soundtrack lost? Perhaps originally narrated by a live presenter...) but interesting and entertaining.